2 Answers:

The mattress will be marketed as two-sided or flippable. When you look at it in a showroom it will have the quilt panel on both sides instead of the non-skid cover on one side. It's pretty evident.

Remember that just because a mattress is two-sided doesn't mean that it will be better than a one-sided, and vice versa. It all comes down to componentry and assembly. Back in the day we had plenty of lousy two-sided products, and today we unfortunately see too many mattresses, one-and two-sided, using lower density foams and not taking the time to properly assemble their products. The end result is what you have.

The onus is upon you to vet brands, retailers or web sites making grandiose claims. Remember, reviews are not research.

Building on Jeff's answer, here is a picture of a two-sided mattress (taken from the Serta Hotel Collection). As you can see, a two-sided mattress will have symmetrical stitching on both sides. On a pillow-top model, like the one shown, there will be a pillow-top on both the top and bottom of the mattress:

By contrast, a one-sided mattress (also a pillow-top, in this case) will have a sleep surface on only one side:

Regarding Jeff's other comments about two-sided versus one-sided, we agree with everything Jeff said in terms of the need to evaluate each mattress on its own merits.

That said, we feel it's worth adding that -- all else being equal -- a two-sided mattress should perform noticeably better at resisting body impressions, which is the number one complaint amongst mattress owners today. Of course, any longevity benefits will only be realized if you make the effort to regularly flip the mattress, which is a complaint some people have about two-sided mattresses. :)